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Goodmorning. I'm reading an article by Arnaud Beauville talking about the surfaces of general type. I've found this term and i'm not sure about the translation: What does it mean a " pinceau de courbes"?

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As Nicky Hekster has rightly said, this translates as pencil of curves.

In case evidence is required for this claim, here is a monograph by O. Wittenberg whose French title is

Intersections de deux quadriques et pinceaux de courbes de genre 1

with the English subtitle

Intersections of two quadrics and pencils of curves of genus 1

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  • $\begingroup$ Note that the original French, which refers to a paintbrush, makes a lot more sense! I always wondered why we call this thing a pencil... fr.wiktionary.org/wiki/pinceau $\endgroup$
    – hunter
    Dec 15, 2014 at 11:39
  • $\begingroup$ @hunter: I've always wondered about "paintbrush" --- why is that more descriptive of a 1-dimensional linear system? I would be glad to hear your interpretation! $\endgroup$
    – user64687
    Dec 15, 2014 at 11:40
  • $\begingroup$ It's not a great interpretation -- just that the bristles are curves that aren't perfectly aligned as in a product but are twisty and fringe-y... it's no better a word than "bundle," but that one is taken. $\endgroup$
    – hunter
    Dec 15, 2014 at 11:42
  • $\begingroup$ @hunter: thanks! I like that image. As you say, it certainly makes more sense then "pencil". $\endgroup$
    – user64687
    Dec 15, 2014 at 11:56

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